Derive the formula for the slope of the tangent line to a parametric curve c(t) (x(t), y(t)) using a method different from that presented in the text Assume that x '(t 0 ) and y '(t0) exist and x '(t 0 ) 0 Show that Then explain why this limit is equal to the slope dy dx Draw a diagram showing that...

Since y to and x to exist we have the following limits ...

Derive the formula for the slope of the tangent line to a parametric curve c(t) = (x(t),

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Derive the formula for the slope of the tangent line to a parametric curve c(t) = (x(t), y(t)) using a method different from that presented in the text. Assume that x'(t₀) and y'(t0) exist and x'(t₀) ≠ 0. Show that

y(to+h)-y(to) lim h0 x(to + h) x(to) y' (to) x'(to)

Then explain why this limit is equal to the slope dy/dx. Draw a diagram showing that the ratio in the limit is the slope of a secant line.

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Dec 21, 2023 05:57 AM

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Derive the formula for the slope of the tangent line to a parametric curve c(t) = (x(t),

Question:

y(to+h)- y(to) lim h→0 x(to + h) x(to) y' (to) x'(to)

Step by Step Answer:

Since y to and x to exist we have the following limits ...View the full answer

Calculus

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